x^(2)+ (7)/(3)x = -(5)/(4)

asked by guest
on Oct 08, 2024 at 12:18 pm



You asked:

Solve the equation \({x}^{2} + \frac{7}{3 x} = \frac{-5}{4}\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= - \frac{\sqrt[3]{\frac{63}{2} + \frac{3 \sqrt{7431}}{8}}}{3} + \frac{5}{4 \sqrt[3]{\frac{63}{2} + \frac{3 \sqrt{7431}}{8}}} \approx -1.0193421\\x &= - \frac{5}{8 \sqrt[3]{\frac{63}{2} + \frac{3 \sqrt{7431}}{8}}} + \frac{\sqrt[3]{\frac{63}{2} + \frac{3 \sqrt{7431}}{8}}}{6} + i \left(\frac{5 \sqrt{3}}{8 \sqrt[3]{\frac{63}{2} + \frac{3 \sqrt{7431}}{8}}} + \frac{\sqrt{3} \sqrt[3]{\frac{63}{2} + \frac{3 \sqrt{7431}}{8}}}{6}\right) \approx 0.50967103 + 1.4245328 i\\x &= - \frac{5}{8 \sqrt[3]{\frac{63}{2} + \frac{3 \sqrt{7431}}{8}}} + \frac{\sqrt[3]{\frac{63}{2} + \frac{3 \sqrt{7431}}{8}}}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{63}{2} + \frac{3 \sqrt{7431}}{8}}}{6} - \frac{5 \sqrt{3}}{8 \sqrt[3]{\frac{63}{2} + \frac{3 \sqrt{7431}}{8}}}\right) \approx 0.50967103 -1.4245328 i\end{aligned}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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